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C17×C7⋊(C52⋊C3) #22581968

order8925
automorphism?
homologyAbelianization (H1) = C3×C17 · Schur multiplier (H2) = C5

Aliases

direct productC17×C7⋊(C52⋊C3)
unambiguous semidirect productC7⋊(C17×C52⋊C3)
unambiguous semidirect productC52⋊(C17×ΓL(1,𝔽8))
unambiguous semidirect product(C7×C17)⋊(C52⋊C3)
unambiguous semidirect product(C52×C17)⋊ΓL(1,𝔽8)

Splittings

Fitting, socle, HallC52×C7×C17 ⋊ C3
derived, HallC52×C7 ⋊ C3×C17
HallC52×C17 ⋊ ΓL(1,𝔽8)
HallC7×C17 ⋊ C52⋊C3
SylowC52 ⋊ C17×ΓL(1,𝔽8)
SylowC7 ⋊ C17×C52⋊C3

Subgroups

subgroupG/H
center, hypercenterC17C7⋊(C52⋊C3)
commutator, hypocenterC52×C7C3×C17
FrattiniC1G
Fitting, socleC52×C7×C17C3
LCSG ▷ C52×C7
UCSC1 ◁ C17

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1037 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC17×#11760386, C17⋊#11760386, C17×(C5⋊D5)⋊ΓL(1,𝔽8), …
maximal normal subgroup ofC17×#11760386, C17⋊#11760386, C17×(C5⋊D5)⋊ΓL(1,𝔽8), …
maximal quotient ofC2×C17×C7⋊(C52⋊C3), C17×C7⋊(C52⋊C9), C3×C17×C7⋊(C52⋊C3), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8925, 4);